{
  "id": 1648,
  "curve_key": "25273977025:-3693087951538625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-526541188",
    "4274187959156"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 71.8591233817366,
  "faltings_height": 3.9514580621043898,
  "conductor": "267725942025",
  "bad_primes": [
    "3",
    "5",
    "17",
    "41",
    "79",
    "241",
    "269"
  ],
  "discriminant": "1449918186048699063342890625",
  "regulator": "787.361799948194162486451322196085973916377135082",
  "points": [
    [
      "33655/4",
      "-5338509/8"
    ],
    [
      "-109946/9",
      "80639480/27"
    ],
    [
      "661256/25",
      "370269831/125"
    ],
    [
      "18839",
      "-1029828"
    ],
    [
      "-59165/4",
      "-23708539/8"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/4. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 02:23:19",
  "updated_at": "2026-09-25 02:23:19"
}